Problem: Solve for $x$ and $y$ using elimination. ${3x+5y = 55}$ ${3x-4y = -17}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${3x+5y = 55}$ $-3x+4y = 17$ Add the top and bottom equations together. $9y = 72$ $\dfrac{9y}{{9}} = \dfrac{72}{{9}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {3x+5y = 55}\thinspace$ to find $x$ ${3x + 5}{(8)}{= 55}$ $3x+40 = 55$ $3x+40{-40} = 55{-40}$ $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ You can also plug ${y = 8}$ into $\thinspace {3x-4y = -17}\thinspace$ and get the same answer for $x$ : ${3x - 4}{(8)}{= -17}$ ${x = 5}$